The general concept of proportional plus integral plus derivative (PID) control is well known in the art. This type of control, while originally used in time mechanisms and steam engine governors, was first described in a mathematical context early in the 20th century. Utilization of PID control led to further development of the concept resulting in the incorporation of PID controllers in a substantial majority of process control applications.
Evolution of the PID controller has led to a current abundance of variants of the basic algorithm. These variants have resulted from restrictions imposed by available hardware. Three principle forms of the PID algorithm are the parallel algorithm (equation 1), the non-interacting algorithm (equation 2), and the interacting algorithm (equation 3), shown below: ##EQU1## Three variants of these basic PID algorithms exist. These algorithm variants can be either position or velocity type, the derivative can be calculated on an error signal or an actual measurement, and the derivative can be calculated directly or through the use of a lead lag.
Equations 1, 2 and 3, as shown above, are written in positional form. In corresponding velocity equations, the error signal is replaced with a change in the error signal and a change in control effort is calculated according to the standard equations 1, 2 and 3. This change in control effort is integrated over time to generate a control effort. In normal operating modes there is no performance difference between the positional algorithm and its velocity counterpart. However, during saturation, when the control effort becomes constrained by one of its limits, the behavior of the foregoing two algorithms is quite different. The velocity type algorithm will move away from its constraints as soon as the absolute value of the error signal on which it is acting decreases. In contrast, a positional type algorithm will not move away from its constraints until the sign of the error signal changes.
Equations 1, 2 and 3 are written to apply derivative action to the error signal. One popular variant of these algorithms is to replace the error signal with the process measurement in the derivative calculation. This change results in smoother transition of the process between setpoint values while not adversely effecting disturbance rejection.
In addition, equations 1, 2 and 3 are written in a form that calculates the derivative contribution directly. Typically, this calculation is implemented in conjunction with a first order filter operating at a time constant of 10% of the derivative time. Equation 4, shown below, illustrates this implementation of the derivative calculation. This modification is made to minimize the effect of process noise on the control signal: ##EQU2##
Another common modification of the PID algorithm is external reset. This variation of equation 3 substitutes an external measurement for the control output in the integral equation. This modification is used to prevent wind-up of the integral term resulting from saturation of the inner loop of cascade control strategies.
Prior art industrial PID controllers allow a user to select between the various algorithm forms only by selection of actual hardware. Thus, the hardward utilized determines the forms of algorithms available in a controller. Because of this limitation, it has been desirable to develop a PID controller which produces a multiplicity of algorithm forms not limited by the hardware utilized.